Question

If $|x+5|\ge 10$ , then

• A. $x\in (-15,5]$
• B. $x\in (-5,5]$
• C. $x\in (-\infty ,-15]\cup [5,\infty )$
• D. $x\in [-\infty ,-15]\cup [5,\infty )$

Answer 1

Answer: (C)

Given $|x+5|\ge 10$
$\Rightarrow x+5\le -10$ or $x+5\ge 10$
$\Rightarrow x\le -15$ or $x\ge 5$
$\Rightarrow x\in (-\infty ,-15]\cup [5,\infty )$